At the end of the module the student should:
· Know the terminology associated with vectors in two and three dimensions.
· Be able to find equations of lines and planes.
· Use vector methods to prove simple geometrical results.
· Be able to manipulate matrices and determinants.
· Be able to solve systems of simultaneous linear equations by several methods.
· Know how to find eigenvalues and eigenvectors, and carry out matrix diagonalisation.
· Be able to solve first order systems of homogeneous linear differential equations.
· Know and understand the terminology associated with vector spaces
· Understand and be able to apply the relationship between linear maps and matrices.
· Appreciate the significance of the eigenvalues and eigenvectors of a linear map.
· Understand quadratic and bilinearforms, and their representation by matrices.
· Recognise the equation of a conic, and know how to find its principal axes.
· Understand the concepts of inner product and orthogonality, for vector spaces over the real numbers, complex numbers and finite fields.
· Be able to formulate simple proofs of results similar to those covered in the course.